If you bite off more than you can chew, you take on more responsibilities than you can manage. 'Don't bite off more than you can chew' is often used to advise people against agreeing to more than they can handle.

If people are boxing and coxing, they are sharing responsibilities so that one of them is working while the other isn't. It can also be used when couples are sharing a house, but their relationship has broken down and when one is at home, the other stays out.